Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-5y &= 3 \\ 2x+8y &= -7\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $8y = -2x-7$ Divide both sides by $8$ to isolate $y$ $y = {-\dfrac{1}{4}x - \dfrac{7}{8}}$ Substitute this expression for $y$ in the first equation. $-x-5({-\dfrac{1}{4}x - \dfrac{7}{8}}) = 3$ $-x + \dfrac{5}{4}x + \dfrac{35}{8} = 3$ Simplify by combining terms, then solve for $x$ $\dfrac{1}{4}x + \dfrac{35}{8} = 3$ $\dfrac{1}{4}x = -\dfrac{11}{8}$ $x = -\dfrac{11}{2}$ Substitute $-\dfrac{11}{2}$ for $x$ back into the top equation. $+ \dfrac{11}{2}-5y = 3$ $\dfrac{11}{2}-5y = 3$ $-5y = -\dfrac{5}{2}$ $y = \dfrac{1}{2}$ The solution is $\enspace x = -\dfrac{11}{2}, \enspace y = \dfrac{1}{2}$.